Initial Questions

In this episode, the biggest questions come on the flop. Zach, Andrew, and I all agree that a turn check is best since I think a bet here is likely only getting called by better. Preflop, a 4-bet seems clear and we will discuss the merits of different sizings. Calling the jam is mostly a question of "does villain ever bluff". Since there are only 6 likely value combos and Andrew only needs 15.6% equity to call, our decision really is that simple. It's not something we will be able to concretely answer here. More simply put, villain should sometimes bluff, but probably isn't. My experience would dictate a fold here, but a call is not difficult to justify when we need less than 1.5 bluff combos to be breaking even.

So let's briefly discuss preflop and then get right to the meat of the hand, what to do on this flop.

Preflop

I think our preflop decision can be boiled down to the following question. Would we like to bet large enough to put MP into a push/fold scenario, or bet a sizing where MP can sometimes call and invite other players into the pot. Now, I'm not assuming that the Button or BB never has something they can call MP's shove or that they never call our larger raise to around 420 after MP folds. However, I think this is the case for some players, and it will happen the majority of the time. For the sake of this analysis, we will assume EV is roughly zero for any additional play against those villains.

First, let's try and get a baseline EV for when we raise preflop slightly larger to force MP into a push/fold scenario. Of course, this assumes MP never flats a raise to 425 which may be false, but let's analyze it as a push/fold. Whenever Button or BB get's involved after this larger raise, we will call our EV for the whole hand 0. Let's say this happens about 10% of the time which may be on the high side. That means we get 90% of our EV when we treat BB and Button as dead money and play against just MP (in a world where MP plays the same as if BB and Button were still in the hand).

So let's take a look at MP's 3bet range. Given how splashy this player is reputed to be, I'm going to have him 3-bet a wide value range along with 50% of all reasonable 3-bet bluff combos and 25% of some less reasonable 3-bet bluffs.

When we 4-bet to 425 and MP shoves a range of ATs+, AQo+, TT+, and folds the rest, our EV from this raise is $197. It's notable that most of that value comes from the dead money and the times MP folds, since we are only a 51.6% favorite against that range. Applying our 10% removal, we would need our smaller 3-bet to result in more than $180 in EV to be correct.

Since we are OOP, let's optimistically say we can realize our equity and call that our EV. MP will 4bet JJ+, AQ+, and call with the following range.

To simplify things, let's say that Button and BB call with AQs, and JJ-55 when MP flats or folds and folds whenever MP shoves (starting to notice the complexity of multiway pots?!). In that model, our bet generates $58 in EV. Now this number is quite off since we will sometimes fold out hands Button of BB calls with and then decides to fold to our raise. Let's add 22-44 and AJs to their 3-bet flatting range that they will fold to our 4-bet when MP folds and see how our EV looks.

With these adjustments which seem realistic, our EV shoots up closer to $90. If we can outplay our opponent's somewhat postflop, then maybe $100 is reasonable. Still, I think this clearly demonstrates the superiority of 4-betting to a larger size given our assumptions about how our opponents will respond.

The Flop

OTF, it seems we are stuck between a rock and a hard place. In the recording, Andrew felt that he had more than enough equity to call the MP's shove if BB folds. This is probably true, since Andrew has 35% equity against the flatting range I gave MP, a range that connects extremely well with this board. There is probably a wider distribution of possibilities in that range, most of which connect less well with the board.

However, Andrew also felt the BB would have this same read. Considering BB should have a lot of pairs, it seems likely that BB would continue with most of them. Once BB commits $580 or so to a $1700 pot, it's not inconceivable that he would stack off with JJ/99/77 beyond the fact that he has TT and 88 squarely in his range.

As discussed on the podcast, there are three plausible lines in my mind. Lead the flop, check/call MP shove after BB folds, or c/r if MP shoves and BB calls.

Since we have already shown that c/c when MP shoves and BB folds is +EV, let's examine the case where MP shoves and we jam over BB's call. In this scenario, we are risking $1860 to win $2215. If we give ourselves a generous 50% equity against MP here, then we will win $1107 whenever BB folds. Whenever MP calls with a set, we lose about $1772 (runner runner straight outs). We can figure out the necessary fold percentage using the equation (1107)(x)-(1772)(1-x)=0. Here, x=.6155, so we need about 62% folds from BB if BB only calls sets and we have 50% equity against BB. If MP only calls JJ-77 and folds 77, 99, JJ, then we are getting 66% folds. Mathematically, this play is +EV given our assumptions. However, if we have closer to 35% equity against MP as our assigned range suggests, the play is a disaster. It's also a disaster if BB ever finds a call with JJ or any other hand that beats us.

So option 3 is possibly ok, probably bad. If MP ships and BB calls, I'm folding. Before giving final considerations about checking, let's examine a lead. Leading this hand is basically a semibluff since we should have equity against a calling range, but we prefer folds. MP seems likely to have three combo that crush us: TT, 88, and 44 don't seem likely to 3bet preflop. Therefore, I think we can expect to have 4 outs on average against a MP call when we lead here. This accounts for times we face TT as well as times we are up against an AT or KT type hand. This gives us around 20% equity when called by MP.

I think the success of the lead roughly correlates to the likelihood that BB will fold a one pair hand. I think a lot of players will feel barrels coming and get away cheaply. Against that type of player where we can expect folds from non-sets when BB has a range of AQs, JJ-66, our lead will be very profitable. Even if we get called from behind by MP 50% of the time and lose our bet whenever BB calls with a set, we make $310 on a lead of 560. If MP only calls 30% of the time, we make $510 on this lead. Of course, this is a pretty optimistic view of BB's play, but we have a strong range, so BB calling with JJ here is not trivial. Against an opponent who will play extremely tight in the BB postflop in this spot, a lead is going to be printing money.

There are some other benefits to checking we did not discuss. The flop will check through at some percentage. We may turn a pair or find a profitable bluff OTT when BB checks twice. However, I feel that based on player descriptions we are going to see a MP shove and a BB call a very large percentage of the time. Considering that our EV when we fold is 0, I think a lead is clearly going to be better even if a $310 in EV is unrealistically high.

Conclusions

I think the flop reinforces a somewhat basic concept that can get clouded in balancing our own range. When our opponent's fold a lot and we have a hand behind their range, we should probably bet. We are leveraging the threat of additional bets to get strong bluffcatchers to fold. Keep in mind that good opponents are likely to have a range that calls the flop and folds the turn. I think BB should be calling JJ and 99 along with TT and 88. We don't really have a range advantage on this board since BB should have more sets, so we can't really barrel. Against savvy opponents who realize that, I think a check is much better with our whole range. However, against an opponent who will not realize this and fold one pair hands, rip it.